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Update Memory usage of st wslda authored by Gabriel Wlazłowski's avatar Gabriel Wlazłowski
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# Arithmetics
Static codes support two types of arithmetics:
* `double complex`: `ELEMENT_SIZE=16B`
default mode: matrix elements of hamiltonian are assumed to be of complex numbers.
default mode: matrix elements of the Hamiltonian are assumed to be of complex numbers.
* `double`: `ELEMENT_SIZE=8B`
if you know that matrix elements, as well as the solution, will be real numbers (for examples based on symmetries of your problem) you can speed-up the calculation process by switching to double arithmetics. To do this you need to activate in [predefines.h](https://gitlab.fizyka.pw.edu.pl/wtools/wslda/-/blob/public/st-project-template/predefines.h) flag:
if you know that matrix elements, as well as the solution, will be real numbers (for examples based on symmetries of your problem) you can speed-up the calculation process by switching to double arithmetics. To do this, you need to activate in [predefines.h](https://gitlab.fizyka.pw.edu.pl/wtools/wslda/-/blob/public/st-project-template/predefines.h) the flag:
```c
/**
* activate this if you know that Hamiltonian matrix is real,
* the code will utilize it in order to speed-up the calculations
* Activate this if you know that the Hamiltonian matrix is real.
* The code will utilize it in order to speed up the calculations by a factor of 4x (approximately)
* */
#define MATRIX_IS_REAL
// #define HAMILTONIAN_IS_REAL
```
# st-wslda-3d
3D version of the code diagonalizes matrix of size:
3D version of the code diagonalizes a matrix of size:
`MATRIX_DIM = NX*NY*NZ*2`.
Memory needed store this matrix in memory is
The memory needed to store this matrix in memory is
`MATRIX_SIZE = MATRIX_DIM*MATRIX_DIM*ELEMENT_SIZE`.
To execute diagonalization routine `st-wslda-3d` code needs at most:
`REQUIRED_MEMORY < 4*MATRIX_SIZE`,
Factor 4 accounts for storage for matrix, storage for eigen-vectors, working space which depends on selected [diagonalization engine](Setting up diagonalization engine) and execution parameters.
To execute the diagonalization routine `st-wslda-3d` code needs:
`REQUIRED_MEMORY = k*MATRIX_SIZE`,
Factor `k` is in [3,10] and accounts for storage for matrix, storage for eigen-vectors, working space, which depends on the selected [diagonalization engine](Setting-up-diagonalization-engine), and execution parameters.
# st-wslda-2d
In (quasi) 2D formulation of the problem diagonalization of full hamiltonian matrix factorizes into a series of `max(NZ/2,1)` diagonalizations of matrices of size (`NZ/2` arises from fact that there is the degeneracy of states with respect to sign of $`k_z`$ wave-vectors):
In (quasi) 2D formulation of the problem, diagonalization of the full Hamiltonian matrix factorizes into a series of `max(NZ/2,1)` diagonalizations of matrices of size (`NZ/2` arises from the fact that there is the degeneracy of states with respect to the sign of $`k_z`$ wave-vectors):
`MATRIX_DIM = NX*NY*2`
and the corresponding matrix size is
`MATRIX_SIZE = MATRIX_DIM*MATRIX_DIM*ELEMENT_SIZE`.
Number of matrices diagonalized simultaneously is:
The number of matrices diagonalized simultaneously is:
`NUMBER_OF_SIMULTANUES_DIAGONALIZATIONS = np / (p*q)`
where `np` is number of MPI processes (provided to mpi execution command) and `p` and `q` are input file parameters.
To execute diagonalization routine `st-wslda-2d` code needs at most:
`REQUIRED_MEMORY < 4*MATRIX_SIZE*NUMBER_OF_SIMULTANUES_DIAGONALIZATIONS`.
where `np` is the number of MPI processes (provided to the mpi execution command) and `p` and `q` are input file parameters.
To execute the diagonalization routine `st-wslda-2d` code needs:
`REQUIRED_MEMORY = k*MATRIX_SIZE*NUMBER_OF_SIMULTANUES_DIAGONALIZATIONS`.
*Note*: if `p` and `q` are not specified in the input file, by default `st-wslda-2d` will select the values that provide the highest parallelization (maximization of a number of simultaneous diagonalization). It means the highest memory request.
*Note*: if `p` and `q` are not specified in the input file, by default `st-wslda-2d` will select the values that provide the highest parallelization (maximization of the number of simultaneous diagonalizations). It means the highest memory request.
# st-wslda-1d
In (quasi) 1D formulation of the problem diagonalization of full hamiltonian matrix factorizes into a series of `max(NY*NZ/4,1)` diagonalizations of matrices of size:
In (quasi) 1D formulation of the problem, diagonalization ofthe full Hamiltonian matrix factorizes into a series of `max(NY*NZ/4,1)` diagonalizations of matrices of size:
`MATRIX_DIM = NX*2`
and the corresponding matrix size is
`MATRIX_SIZE = MATRIX_DIM*MATRIX_DIM*ELEMENT_SIZE`.
Number of matrices diagonalized simultaneously is:
The number of matrices diagonalized simultaneously is:
`NUMBER_OF_SIMULTANUES_DIAGONALIZATIONS = np / (p*q)`
where `np` is number of MPI processes (provided to mpi execution command) and `p` and `q` are input file parameters.
To execute diagonalization routine `st-wslda-1d` code needs at most:
`REQUIRED_MEMORY < 4*MATRIX_SIZE*NUMBER_OF_SIMULTANUES_DIAGONALIZATIONS`.
where `np` is the number of MPI processes (provided to the mpi execution command) and `p` and `q` are input file parameters.
To execute the diagonalization routine `st-wslda-1d` code needs at most:
`REQUIRED_MEMORY = k*MATRIX_SIZE*NUMBER_OF_SIMULTANUES_DIAGONALIZATIONS`.
*Note*: if `p` and `q` are not specified in the input file, by default `st-wslda-1d` will select the values that provide the highest parallelization (maximization of a number of simultaneous diagonalization). It means the highest memory request.
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*Note*: if `p` and `q` are not specified in the input file, by default `st-wslda-1d` will select the values that provide the highest parallelization (maximization of the number of simultaneous diagonalizations). It means the highest memory request.
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